More Sums on a Triangle

.
/a\
.---.
/b\c/d\
.---.---.
/e\f/g\h/i\
.---.---.---.

Can you place the numbers 1-9 in the locations a-i on the triangle, such
that every row of 5 smaller triangles (there are 3: abcef, acdhi, efghi)
has the same sum? How many different sums are possible?

Can you place the numbers 1-9 in the locations a-i on the triangle,
such that the six rows (three of 5 triangles, three of 3 triangles)
have different sums? Consecutive sums?